Design of stabilizing dynamic output feedback controllers for hidden Markov jump linear systems

Presented at the 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, December 17-19, 2018International audienceIn this letter, we investigate the design of stabilizing dynamic output feedback controllers for Markov jump linear systems considering a context of partial information on the Markov chain. We assume that the mode of operation of the system is not available, but only an estimation provided by a detector in the spirit of hidden Markov models. We present new nonlinear matrix inequalities conditions for the design of stabilizing dynamic controllers that depend only on the estimation, and by means of some interesting properties of this new condition, we are able to provide a type of ad hoc separation procedure involving linear matrix inequalities in which the controller is obtained via a two-stage algorithm. First a stabilizing state feedback gain depending only on the estimation is calculated and used as an input in the second step for obtaining the remaining controller parameters. The final stabilizing controller is composed by both the state feedback gain of the first stage and the dynamic system calculated in the last stage. We present a numerical example in the context of systems subject to failures in order to illustrate our results